Steady state analysis for a relaxed cross diffusion model

Abstract

In this article we study the existence the existence of nonconstant steady state solutions for the following relaxed cross-diffusion system [fórmula] with a bounded smooth domain, n the outer unit normal to @ , > 0 denote the relaxation parameter. The functions a(v), b(u) account for nonlinear crossdiffusion, being a(v) = 1 + v-y , b~u) = 1 + u-ñ with y, n > 1 a model example. We give conditions for the stability of constant steady state solutions and we prove that under suitable conditions Turing patterns arise considering as a bifurcation parameter.